Theorems · Theorem · ring theory
OreLocalization.expand
∀ {R : Type u_1} [inst : Monoid R] {S : Submonoid R} [inst_1 : OreLocalization.OreSet S] {X : Type u_2}
[inst_2 : MulAction R X] (r : X) (s : ↥S) (t : R) (hst : t * ↑s ∈ S), r /ₒ s = t • r /ₒ ⟨t * ↑s, hst⟩A fraction r /ₒ s is equal to its expansion by an arbitrary factor t if t * s ∈ S.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement and proof · cited by 3,086
- mul_assocproof · cited by 1,667
- MulActionstatement and proof · cited by 1,294
- SemigroupAction.mul_smulproof · cited by 291
- OreLocalization.OreSetstatement and proof · cited by 92
- OreLocalizationstatement · cited by 90
- OreLocalization.oreDivstatement · cited by 72
- Submonoid.smul_defproof · cited by 42
Cited by4
Results whose statement or proof uses this declaration.
- OreLocalization.expand'proof · cited by 3
- OreLocalization.smul_addproof · cited by 1
- OreLocalization.add_smulproof · cited by 1
- OreLocalization.add_assocproof · cited by 0